We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a LittlewoodRichardson rule for decomposing tensor products of irreducible representations. The new model is based on the ...

Let F be a p-adic field of characteristic 0, and let A be an F -central division algebra of dimension dA over F . In the paper we first develop the representation theory of GL(m,A), assuming that holds the conjecture which claims that unitary parabolic induction is irreducible for GL(m,A)’s. Among others, we obtain the formula for characters of irreducible unitary representations of GL(m,A) in ...

A central topic in representation theory is to understand the irreducible modules. In this paper we are concerned with nite dimensional irreducible modules of quantized hy-peralgebras and of hyperalgebras. Recently, big progress has been made on the characters of the irreducible modules, namely the Lusztig's conjectural formula for the characters is true for quantized hyperalgebras and is true ...

A well-known property of irreducible characters of finite groups is the fact, proved by Burnside, that if G is a finite group and % : G −→ GL(E) is an irreducible complex representation of dimension dim(%) > 2, then there exists some g ∈ G such that χ%(g) = Tr %(g) is zero. A common argument to prove this relies on the following result (also due to Burnside) on representations of finite cyclic ...